An ad hominem argument, also known as argumentum ad hominem (Latin:
"argument to the person", "argument against the man") consists of
replying to an argument by attacking or appealing to the person making the argument,
rather than by addressing the substance of the argument.

You claim that this man is innocent, but you cannot be trusted since you
are a criminal as well.

You feel that abortion should be legal, but I disagree, because you are
uneducated and poor.

You can't believe Jack when he says there isn't any God because he
doesn't even have a job.

An appeal to authority or argument by authority is a type of argument in
logic, consisting on basing the truth value of an otherwise unsupported assertion on the
authority, knowledge or position of the person asserting it.

Appeal to consequences is an argument that concludes a premise (typically
a belief) to be either true or false based on whether the premise leads to desirable or
undesirable consequences. This is based on an appeal to emotion and is considered to be a
form of logical fallacy, since the appeal of a consequence does not address the truth
value of the premise.

"Atheism must be erroneous: it denies eternal happiness after
death."

"Religion is the opiate of humanity: if it were true, nobody would
have free will."

Appeal to emotion is a logical fallacy which uses the manipulation of the
listener's emotions, rather than valid logic, to win an argument. This kind of appeal to
emotion is a type of red herring and encompasses several logical fallacies, including:

An appeal to fear is a logical fallacy in which a person attempts
to create support for her or his idea by increasing fear and prejudice toward a
competitor. The appeal to fear is extremely common in marketing and politics.

"Nobody ever got fired for buying IBM"

"If we don't introduce National ID cards, the terrorists have
won."

"If the defendant is acquitted, there will be riots. Therefore, he
is guilty."

An appeal to pity is a logical fallacy in which someone tries to
win support for their argument or idea by exploiting their opponent's feelings of pity or
guilt. The appeal to pity is a specific kind of appeal to emotion.

"I hope you like my proposal. It took me six years to write and I
don't know what I'd do if you rejected it."

"I really deserve a raise. Unless I make more money I may lose my
home."

"I hope you find the defendant not guilty of embezzlement. Just look
at the poor guy, he's in a wheelchair. Show some sympathy!"

In logic, begging the question, also known as circular reasoning and by
the Latin name petitio principii, is an informal fallacy found in many attempts at logical
arguments. An argument which begs the question is one in which a premise presupposes the
conclusion in some way. Such an argument is valid in the sense in which logicians use that
term, yet provides no reason at all to believe its conclusion.

"The Bible says God exists, and the Bible must be right since it is
the revealed word of God, so God exists." Obviously enough, no one who doubts the
conclusion has any reason to accept the second premise, which presupposes it. This is, of
course, a blatant example meant solely to illustrate the fallacy; less contrived instances
may be much more subtle.

A version of our first example that constitutes circular reasoning in
this strict sense would involve asserting both:

The Bible tells me that faith in God is a good basis for forming beliefs

In general, what the Bible says is true

Therefore, faith in God is a good basis for belief

and

Faith in God is a good basis for forming beliefs

My faith in God tells me that, in general, what the Bible says is true

A biased sample is one that is falsely taken to be typical of a
population from which it is drawn. Someone saying "Everyone liked that movie!"
might not mention that the "everyone" was them and three of their friends, or a
group of the star's fans.

I wouldn't like to go to America because of all the gun crime, we see it
on the news all the time.

Why do young people all take drugs and go around mugging old ladies? You
read about it in the paper all the time!

The logical fallacy of accident, also called destroying the exception, is
a deductive fallacy occurring in statistical syllogisms (an argument based on a
generalization) when an exception to the generalization is ignored.

Cars should never exceed the speed limit.
Police cars are cars. Therefore, police cars should
never exceed the speed limit.

Cutting people with a knife is a crime.
Surgeons cut people with knives.
Surgeons are criminals

The fallacy of the single cause, also known as joint effect or causal
oversimplification, is a logical fallacy of causation that occurs when it is assumed that
there is one, simple cause of an outcome when in reality it may have been caused by a
number of only jointly sufficient causes.

Often after a tragedy it is asked, "What was the cause of
this?" Such language implies that there is one cause, when instead there were
probably a large number of contributing factors. However, having produced a list of
several contributing factors, it may be worthwhile to look for the strongest of the
factors, or a single cause underlying several of them.

Hasty generalization, also known as fallacy of insufficient statistics,
fallacy of insufficient sample, fallacy of the lonely fact, leaping to a conclusion, hasty
induction, law of small numbers, unrepresentative sample, is the logical fallacy of
reaching an inductive generalization based on too little evidence. It commonly involves
basing a broad conclusion upon the statistics of a survey of a small group that fails to
sufficiently represent the whole population.

"I loved the hit song, therefore I'll love the album it's
on". Fallacious because the album might have one good song and lots of filler.

"This Web site looks OK to me on my computer; therefore, it will
look OK on your computer, too". Fallacious because different computers may present
content differently.

"I got into a fight with a bunch of Asians today. They all knew
10 Animal Huo style Kung Fu. This means that all Asians know 10 Animal Huo style Kung
Fu."

Irrelevant conclusion is the logical fallacy of presenting an argument
that may in itself be valid, but which proves or supports a different proposition than the
one it is purporting to prove or support.

A red herring is a deliberate attempt to change the subject or divert the
argument from the real question at issue;

For instance, “Senator Jones should not be held accountable for
cheating on his income tax. After all, there are other senators who have done far worse
things.” Another example “I should not pay a fine for reckless driving. There are many
other people on the street who are dangerous criminals and rapists, and the police should
be chasing them, not harassing a decent tax-paying citizen like me.”

Baseball player Mark McGwire just retired. Clearly, he will end up in the
Hall of Fame. After all, he's such a nice guy, and he gives a lot of money to all sorts of
charities. (Friendliness and charity are not qualifications for induction into the Hall of
Fame, therefore they do not support the conclusion.)

In philosophy, a logical fallacy or a formal fallacy is a pattern of
reasoning which is always or at least most commonly wrong. This is due to a flaw in the
structure of the argument which renders the argument invalid. A formal fallacy is
contrasted with an informal fallacy, which has a valid logical form, but is false due to
one or more of its premises being false.

The term fallacy is often used more generally to mean an argument which
is problematic for any reason, whether it be a formal or an informal fallacy.

The presence of a formal fallacy in a deductive argument does not imply
anything about the argument's premises or its conclusion. Both may actually be true, or
even more probable as a result of the argument (e.g. appeal to authority), but the
deductive argument is still invalid because the conclusion does not follow from the
premises in the manner described.

A non sequitur is a conversational and literary device, often used for
comical purposes (as opposed to its use in formal logic). It is a comment which, due to
its lack of meaning relative to the comment it follows, is absurd to the point of being
humorous or confusing. Its use can be deliberate or unintentional. Literally, it is Latin
for "it does not follow."

A good example of this device can be seen in an episode of the Micallef
Programme which features a game show segment called Non-Sequitur Family Feud. The
presenter asks the question "Name ten things you plug in", to which the
contestant answers correctly with a list of ten random phrases, including mules, Lewis
Carroll, 1832 and "I like butterscotch".

The non sequitur can be understood as the converse of cliché. To
illustrate: in theatre, traditional comedy and drama depend on the ritualization—that
is, the predictability—of human emotional experiences. In contrast, the theatre of the
absurd depends upon the disjunction—that is, the unpredictability—of that experience.
Predictability in its most extreme form is cliché; unpredictability, then, expresses
itself most naturally as non sequitur.

An overwhelming exception is a logical fallacy similar to a hasty
generalization. It is a generalization which is accurate, but comes with one or more
qualifications which eliminate so many cases that what remains is much less impressive
than the initial statement might have led one to assume.

"Our foreign policy has always helped other countries, except of
course when it is against our National Interest..." (The false implication is that
our foreign policy always helps other countries).

"All right, but apart from the sanitation, the medicine, education,
wine, public order, irrigation, roads, a fresh water system, and public health, what have
the Romans ever done for us?" (The attempted implication (fallaciously false in this
case) is that the Romans did nothing for us). This is a quotation from Monty Python's Life
of Brian.

Proof by verbosity is a term used to describe an excessively verbose
mathematical proof that may or may not actually prove the result. Such proofs are most
often presented by students who don't fully grasp the concepts they are writing about.
Students presenting such proofs often either hope to hide their lack of understanding or
are uncertain how extensive their proof is expected to be.

Proof by verbosity should not be confused with proof by exhaustion, the
latter being a valid form of proof. The difference lies in that a proof by exhaustion is
used when a number of dissimilar cases must be independently proven, whereas a proof by
verbosity tends to be repetitive, with many overlapping proofs for specific cases of a
more general problem.

It suggests that an action will initiate a chain of events culminating in
an undesirable event later. The argument is sometimes referred to as the thin end of the
wedge or the camel's nose. The slippery slope can be valid or fallacious.

An effective procedure for checking whether a propositional formula is a
tautology or not is by means of truth tables.

Slippery slope can also be used as a retort to the establishment of
arbitrary boundaries or limitations. For example, one might argue that rent prices must be
kept to $1,000 or less a month to be affordable to tenants in an area of a city. A retort
invoking the slippery slope could go in two different directions:

Once such price ceilings become accepted, they could be slowly lowered,
eventually driving out the landlords and worsening the problem.

If a $1,000 monthly rent is affordable, why isn't $1,025 or $1,050? By
lumping the tenants into one abstract entity, the argument renders itself vulnerable to a
slippery slope argument. A more careful argument in favor of price ceilings would
statistically characterize the number of tenants who can afford housing at various levels
based on income and choose a ceiling that achieves a specific goal, such as housing 80% of
the working families in the area.

In logic, a tautology is a statement containing more than one
sub-statement, that is true regardless of the truth values of its parts. For example, the
statement "Either all crows are black, or not all of them are", is a tautology,
because it is true no matter what color crows are.

An effective procedure for checking whether a propositional formula is a
tautology or not is by means of truth tables.

As an efficient procedure, however, truth tables are constrained by the
fact that the number of logical interpretations (or truth-value assignments) that have to
be checked increases as 2k, where k is the number of variables in the formula. Algebraic,
symbolic, or transformational methods of simplifying formulas quickly become a practical
necessity to overcome the "brute-force", exhaustive search strategies of tabular
decision procedures.

In logic, the form of an argument is valid precisely if it cannot lead
from true premises to a false conclusion. An argument is said to be valid if, in every
model in which all premises are true, the conclusion is true. For example: "All A are
B; some A are C; therefore some B are C" is a valid form.

A formula of logic is said to be valid if it is true under every
interpretation (also called structure or model).